Place Value, Multiplication, Division

Using Power of Ten as a tool to Understand:Place ValueMultiplicationDivision

N3.1 Demonstrate understanding of whole numbers to 1000 (concretely, pictorially, physically, orally, in writing, and symbolically) including:· representing (including place value)· describing· estimating with referents· comparing two numbers· ordering three or more numbers.

N4.1 Demonstrate an understanding of whole numbers to 10 000 (pictorially, physically, symbolically) by:· representing· describing· comparing two numbers· ordering three or more numbers.

Place Value

"Zero the Hero" Story

http://www.youtube.com/watch?v=Nvc2PPTlW7k

http://www.rif.org/assets/Documents/readingplanet/ReadAloud_Stories/zero_the_hero.html

Credit to drjean.org

Number Relationships:Anchoring Numbers to 10·Students need a solid foundation of 'ten'·There are many activities to develop this concept.

We are going to experience a few games to practice this concept of 'tenness'.1. Salute 2. Advanced Salutehttp://

www.poweroften.ca/index.php?view=video&id=34%3Agrade-3-salute&option=com_jomtube&Itemid=139

Once students have mastered 'tenness' then they can move to number relationships of larger numbers.

Rounding

Story of Rounding

1 2 3 4 5 6 7 8 9 10

7080 90

83

Who could they be?

A B C D

What numbers do you think are A,B,C, and D and why?

Close, Far and In Between

Which two numbers are closest and why?Which number is closest to 200? Why?Name a number in between any of these two numbers. _____ ______ ______How far apart are 184 and 199? Explain how you know.If these are big numbers, what are some small numbers?List 3 numbers that make these numbers seem small?

Connections to Real -World Ideas

1 752

Population of Langenburg , Germany

Population of Langenburg, Saskatchewan, Canada

1 048

What could we do with these numbers?

Add the numbers in your head. What were the strategies that you used?

Build a number that you see.

37

31

41

12

13

38

19

28

9

22

Build a number that you see.

37

31

41

12

13

38

19

28

9

22

Make 50

Build a number that you see.

815

635

435

565

760

550

365

280

450

185

720

Build a number that you see.

815

635

435

565

760

550

365

280

450

185

720

Make 1 000

N3.3 Demonstrate understanding of multiplication to 5 × 5 and the corresponding division statements including:· representing and explaining using repeated addition or subtraction, equal grouping, and arrays· creating and solving situational questions · modelling processes using concrete, physical, and visual representations, and recording the process symbolically· relating multiplication and division.

N4.3 Demonstrate an understanding of multiplication of whole numbers (limited to numbers less than or equal to 10) by:· applying mental mathematics strategies · explaining the results of multiplying by 0 and 1.

N4.4 Demonstrate an understanding of multiplication of whole numbers (2- or 3-digit by 1 - digit) by:· modeling the distributive property· using personal strategies for multiplication, with and without concrete materials· using arrays to represent multiplication· connecting concrete representations to symbolic representations· estimating products solving problems.

N4.5 Demonstrate an understanding of division of whole numbers(1-digit divisor to 2-digit dividend) by:· using personal strategies for dividing, with and without concrete materials· estimating quotients· explaining the results of dividing by 1· solving problems involving division of whole numbers· relating division to multiplication.

Multiplication and Division

Students should know their doubles before you begin multiplication and division.

http://www.poweroften.ca/index.php?view=video&id=46&option=com_jomtube&Itemid=139

http://www.poweroften.ca/index.php?view=video&id=44&option=com_jomtube&Itemid=139

For example: when examining the 24th

day of a month during calendar time and discussingthe varied groupings possible that equal 24, somestudents will build an array that shows: 4 groups of 6or 4 × 6 = 24. This array should at once be related toall the facts in this family of groupings:• 4 × 6 = 24

• 6 × 4 = 24

• 24 ÷ 6 = 4·24 ÷ 4 = 6

Division should also be taughtalong with multiplication. When an array iscreated or a specific area is calculated, the relevantdivision questions should always be discussed at thesame time.

Some effective teaching strategies for developing multiplication concepts are as follows:• Avoid teaching a multiplication table in a specific order, as this promotes counting strategies.Instead use a doubling strategy such as 2 × 5 = 10, 4 × 5 = 20, and 8 × 5 = 40.• Avoid teaching tables before grade three.

• Teach meaning through grouping, calendar time, and meaningful projects.

• When teaching the multiplication tables, use many varied strategies including:

Ö Forming groupsÖ Making arraysÖ Graphing arrays on cm grid paperÖ Relating multiplication to areaÖ Using number linesÖ Clapping the facts, and using music and rhymes to reinforce multiplication factsÖ Using visual toolsÖ Breaking numbers up• Relate multiplication equations to other questions that are similar and more readily understandable.

• Use kinesthetic approaches (clapping, standing and sitting, and manipulating or handling egg cartons).

(Page 112) Teaching the 5 Times Tables First

1 group of 5

2 groups of 5

bounce ball- rhythmic

How many 5's make 20?

I see...I think...This reminds me of...

http://vimeo.com/15261830

Next teach the 10 times tables.What patterns do you notice?

0 and 15,10,0,1 this leaves 2,3,4,6,7,8,9 (2's are doubles)

You have only half of the remaining due to the commutative property!!!

http://www.poweroften.ca/index.php?view=video&id=42%3Agrade-3-learning-the-difficult-multiplication-facts&option=com_jomtube&Itemid=139

Learning the Difficult Multiplication Facts 6,7,8 (halving and doubling strategy)

8x6= 16x8=8x8=4x8=32....64

64x2=128

18x25=9x50

8x6=486x8=4848 6=848 8=6

16x8=8x8=4x8=32....64

64x2=128

Teach your Fact Families

4 x 27=4(20 +7)=4(20) + (7)=80 + 28=108

Distributive Property

I am thinking of a question :It is a multiple of 4.

The product is greater than 30 and less than 40.The sum of the digits in the product is 5. What is my question?

Show What is my question sheet page 59

4,8,16,20,24,28,32,36,40,

3+2=5 3+6=9The answer is 8x4=32

A hotel has 24 windows on a floor. There are 9 floors. How many windows are there?Is the number of windows more than 240? How do you know? How could you estimate the number of windows? How could you use manipulatives to model the problem?Mental Math ?

Describe a situation when you might divide 50 by 4.

Now describe a situation when you are forming groups but don't divide.

Susan says 45-9-9-9-9-9=0describes division do you agree? Explain.

Partitioning or Fair SharingThe bag has 783 jelly beans, and Maggie and her four friends want to share them equally. How many jelly beans will Maggie and each of her friends each get?

Measurement or Repeated Subtraction ConceptJumbo the elephant loves peanuts. His trainer has 620 peanuts. If he gives Jumbo 20 peanuts each day, how many days will the peanuts last?

Jumbo the elephant loves peanuts. His trainer has 20 peanuts. If he gives Jumbo 5 peanuts each day, how many days will the peanuts last?

Day Number of Peanuts

The bag has 783 jelly beans, and Maggie and her four friends want to share them equally. How many jelly beans will Maggie and each of her friends each get?

Jumbo the elephant loves peanuts. His trainer has 20 peanuts. If he gives Jumbo 5 peanuts each day, how many days will the peanuts last?------------------------------------------------------------------What if he only gave 2 a day, how many days will the peanuts last?

Day Number of Peanuts

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